sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
Tanaka, Toshiaki
arXiv, 0306174 / Harvested from arXiv
Text on arXiv
We propose a systematic method to construct quasi-solvable quantum many-body systems having permutation symmetry. By the introduction of elementary symmetric polynomials and suitable choice of a solvable sector, the algebraic structure of sl(M+1) naturally emerges. The procedure to solve the canonical-form condition for the two-body problem is presented in detail. It is shown that the resulting two-body quasi-solvable model can be uniquely generalized to the M-body system for arbitrary M under the consideration of the GL(2,K) symmetry. An intimate relation between quantum solvability and supersymmetry is found. With the aid of the GL(2,K) symmetry, we classify the obtained quasi-solvable quantum many-body systems. It turns out that there are essentially five inequivalent models of Inozemtsev type. Furthermore, we discuss the possibility of including M-body (M>=3) interaction terms without destroying the quasi-solvability.
Publié le : 2003-06-18
Classification:  High Energy Physics - Theory,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  Quantum Physics 
@article{0306174,
     author = {Tanaka, Toshiaki},
     title = {sl(M+1) Construction of Quasi-solvable Quantum M-body Systems},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0306174}
}

Tanaka, Toshiaki. sl(M+1) Construction of Quasi-solvable Quantum M-body Systems. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0306174/